Which expressions are completely factored?

Select each correct answer.

A. 16a^5−20a^3=4^3(4a^2−5)

B. 24a^4+18=6(4a^4+3)

C. 30a^6−24a^2=3a^2(10a^4−8)

D. 12a^3+8a=4(3a^3+2a)

Answer:

it is a 32-gon

Step-by-step explanation:

Answer:  the correct option is (B) x = 6.

Step-by-step explanation:  Given that x varies inversely as v and x = 48 when v = 8.

We are to find the value of x when v = 64.

Since x varies inversely as v, so we have

[tex]x\propto\dfrac{1}{v}\\\\\\\Rightarrow x=k\dfrac{1}{v}~~~~~~~~~~~~~~~~~~[\textup{where k is the constant of proportionality}][/tex]

When x = 48 and v = 8, then, we get

[tex]48=\dfrac{k}{8}\\\\\Rightarrow k=48\times8\\\\\Rightarrow k=384.[/tex]

So,

[tex]x=\dfrac{384}{v}~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Therefore, when v = 64, then from equation (i), we get

[tex]x=\dfrac{384}{64}=6.[/tex]

Thus, the required value of x is 6.

Option (B) is CORRECT.

The value of x so that lines c and d are parallel lines cut by transversal p is 18.

Transversal lines are lines that passes intersects the two lines on a plane in two different points.

Given are two parallel lines c and d.

p is the transversal line passing through c and d.

The angle at the exterior side of angle 81° is 180° - 81° = 99°

When two parallel lines are intersected by a transversal line, then the angles formed at the corresponding corners of the transversal with each of the parallel line is called corresponding angles.

(3x + 45)° and 99° are corresponding angles.

Corresponding angles are always equal.

(3x + 45)° = 99°

3x = 99 - 45

3x = 54

x = 54 / 3

x = 18

Hence the value of x is 18.

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Answer:

The initial value of the graph is 2. Third option is correct.

Step-by-step explanation:

It is given that A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.

The line is passing through the points (0,2) and (7,5).

The point (0,2) is the y-intercept and graph labeled from 0 to 7, therefore 2 is the initial value.

Slope of line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{7-0}=\frac{3}{7}[/tex]

The equation of line is

[tex]y=mx+b[/tex]

Where, m is slope and b is y-intercept. So the equation of given line is

[tex]y=\frac{3}{7}x+2[/tex]

At initial condition the value of x is 0. So, put x=0.

[tex]y=\frac{3}{7}(0)+2=2[/tex]

Therefore the initial value of the graph is 2. Option 3 is correct.

Answer:

Option 3 rd is correct

Initial value = 2

Step-by-step explanation:

A equation of line is given by:

[tex]y =mx+b[/tex]          ....[1]

where

m is the slope of the line and b is the y-intercept or the initial value

As per the statement:

A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.

It is also given that:

A straight line joins the ordered pair (0, 2) with the ordered pair (7, 5)

Calculate slope:

using formula:

[tex]\text{Slope (m)} = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given ordered pairs we have;

[tex]\text{Slope (m)} = \frac{5-2}{7-0}=\frac{3}{7}[/tex]

y-intercept states that the graph which cut y-axis.

Substitute x =0 and solve for x:

we have given with the ordered pair (0, 2)

⇒y-intercept(b) = 2

Substitute the given values of m and b in [1]

[tex]y = \frac{3}{7}x+2[/tex]

The equation of straight line  joins the ordered pair (0, 2) with the ordered pair (7, 5) is:

[tex]y = \frac{3}{7}x+2[/tex]

The initial value of the function represented by the given graph as shown below is: 2

Final answer:

The notation '+1.25 E -19' represents the number in scientific notation, equivalent to 1.25 × 10^-19.

Explanation:

The notation '+1.25 E -19' is likely intended to be represented the number 1.25 × 10-19, which is an example of scientific notation.

The Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in the decimal form. In this context, 'E' stands for exponent, indicating that the number should be multiplied by 10 and raised to the power of -19.

Therefore, +1.25 E -19 means the number is positive and equals 0.000000000000000000125.

Explanation of mathematical induction proof for two statements and demonstration of P1, Pk, and Pk+1 for another equation.

Mathematical Induction Proof for Statement 1:

Mathematical Induction Proof for Statement 2:

P1, Pk, and Pk+1 for 2 + 4 + 6 + ... + 2n = n(n+1): P1 is true, assume Pk is true, then prove Pk+1 using Pk.

The coefficient of the x-term in the trinomial is C. The sum of -p and -q, which is -p - q. therefore ,option C. The sum of -p and -q, which is -p - q is correct.

When the factors of a trinomial are (x - p) and (x - q), you can find the coefficient of the x-term in the trinomial by multiplying these factors together and paying attention to the x-term.

The product of (x - p) and (x - q) is:

(x - p)(x - q) = x^2 - qx - px + pq

Now, notice that the coefficient of the x-term is the sum of the terms that contain 'x,' which are -qx and -px:

Coefficient of the x-term = -qx - px

This can be factored as:

Coefficient of the x-term = x*(-q - p)

So, the coefficient of the x-term in the trinomial is:

C. The sum of -p and -q, which is -p - q

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Answer:

$70

Step-by-step explanation:

Let's define the expenses first

Fixed expenses are those expenses that remain constant in all months like mortage payments, rents etc

Flexible expenses also called variable expense are expenses that are used for comfortable living like car maintenance o groceries.

Discretionary expenses are the expenses spent on non essential items like movie tickets, outings etc.

Savings are the expenses that are stored for future plans.

Hence, from the given pie chart the money going for optional expenses is $70 ..

By assuming that x = 2 and substituting this into the original equation x^2 + x = 4, we arrive at a contradiction because 4 + 2 ≠ 4. Thus, we conclude through indirect proof that x cannot equal 2.

To give an indirect proof of the statement If x2 + x = 4, then x ≠ 2, we start by assuming the opposite of what we want to prove, which is that x = 2. Our goal is to show that this assumption leads to a contradiction.

Assume that x = 2. Substituting 2 for x in the original equation gives us (2)2 + 2 = 4 + 2 = 6, which is clearly not equal to 4. This contradicts the original equation x2 + x = 4. Since our assumption that x = 2 leads to a false statement, it follows that x cannot be 2, thereby proving the original statement by contradiction.

The method of assuming the negation and arriving at a contradiction shows that the original statement must be true according to the logical principle of indirect proof. Hence, if x2 + x = 4, then indeed x ≠ 2.

The number of grams of fat in 2.5 cups of corn is 19.7.

To find the number of grams of fat in 2.5 cups of corn, we can use the following steps:

Multiply the number of cups of corn by the number of grams of fat per cup:

2.5 cups * 7.87 grams/cup = 19.675 grams

Round the answer to the nearest tenth:

19.675 grams = 19.7 grams

Therefore, there are 19.7 grams of fat in 2.5 cups of corn.

Here are some additional things to consider:

The number of grams of fat in corn may vary depending on the variety of corn and the way it is cooked.

The amount of fat in corn is also affected by the amount of oil that is used when cooking the corn.

If you are concerned about the amount of fat in corn, you can choose to cook it without oil or to use a cooking spray instead of oil.

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Final answer:

The sales tax rate is 4%.

Explanation:

To calculate the sales tax rate for the cinnamon-scented pencils, you first need to determine the amount of sales tax paid and then relate that to the original price of the pencils.

The total cost is given as $5.20, and the original price is $5.00.

The difference between these two amounts is the sales tax paid.

Subtract the original price from the total cost to find the sales tax amount:

$5.20 - $5.00 = $0.20.

Next, to find the sales tax rate, divide the sales tax amount by the original price and multiply by 100 to get a percentage:

Sales Tax Rate = ($0.20 / $5.00) x 100 = 4%

Therefore, the sales tax rate is 4%.